$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 1$ and $ BC = 2x + 13$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 1} = {2x + 13}$ Solve for $x$ $ 4x = 12$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({3}) + 1$ $ BC = 2({3}) + 13$ $ AB = 18 + 1$ $ BC = 6 + 13$ $ AB = 19$ $ BC = 19$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {19} + {19}$ $ AC = 38$